Page:Scientific Papers of Josiah Willard Gibbs.djvu/455

On the Values of Potentials in Liquids for Substances which form but a Small Part of the whole Mass.^[1]

The value of a potential^[2] for a volatile substance in a liquid may be measured in a coexistent gaseous phase,^[3] and so far as the latter may be treated as an ideal gas or gas-mixture,^[4] the value of the potential will be given by the equation (276), ["Equilib. Het. Subs."] which may be briefly written

$\mu ={\text{func}}(t)+at\log \gamma _{\text{gas}},$

[1]

where $\mu$ is the potential of the volatile substance considered, either in the liquid or in the gas, $t$ the absolute temperature, $\gamma _{\text{gas}}$ the density of the volatile substance in the gas and a the constant of the law of Boyle and Charles. Since this last quantity is inversely proportional to the molecular weight we may set

$a={\frac {A}{M}},$

where $M$ denotes the molecular weight, and $A$ an absolute constant (the constant of the law of Boyle, Charles, and Avogadro),^[5] and write the equation in the form

$\mu ={\text{func}}(t)+{\frac {At}{M}}\log \gamma _{\text{gas}},$

[2]

in which the value of the potential depends explicitly on the molecular weight.

The validity of this equation, it is to be observed, is only limited by the applicability of the laws of ideal gases to the gaseous phase; there is no limitation in regard to the proportion of the substance in question to the whole liquid mass. Thus at 20° Cent. the equation may be determined by the potential for water or for alcohol in a mixture of the two substances in any proportions, since the vapor of the mixture may be regarded as an ideal gas-mixture. But at a temperature at which we approach the critical state, the same is not true without limitation, since the coexistent gaseous phase cannot be treated as an ideal gas-mixture. At the same temperature however, if we limit ourselves to cases in which the proportion of water does not exceed ${\tfrac {1}{10}}$ of one per cent., and suppose the density of the

1. The object of this chapter is to show the relation of the doctrine of potentials to van't Hoff's Law (what form van't Hoff's Law takes from the standpoint of the potentials); and to the modern theory of dilute solutions as developed by van't Hoff and Arrhenius. "Equilib. Het. Subs." [this volume], pp. 135–138, 138–144, 164–165, 168–172, 172–184.
2. For the definition of this term see p. 93, also pp. 92–96.
3. In some cases a semi-permeable membrane may be necessary. (Enlarge.) (Is the term coexistent right in this case?)
4. Definition. (Enlarge.)
5. ${\frac {pvM}{mt}}=A,$$pv={\frac {m}{M}}At.$ Is absolute used correctly?